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pyerrors/__init__.py
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@ -6,7 +6,7 @@ It is based on the **gamma method** [arXiv:hep-lat/0306017](https://arxiv.org/ab
- **treatment of slow modes** in the simulation as suggested in [arXiv:1009.5228](https://arxiv.org/abs/1009.5228)
- coherent **error propagation** for data from **different Markov chains**
- **non-linear fits with x- and y-errors** and exact linear error propagation based on automatic differentiation as introduced in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289)
- **real and complex matrix operations** and their error propagation based on automatic differentiation (cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...)
- **real and complex matrix operations** and their error propagation based on automatic differentiation (Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...)
## Getting started
@ -66,17 +66,19 @@ my_m_eff = np.log(my_obs1 / my_obs2)
## Error estimation
The error estimation within `pyerrors` is based on the gamma method introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).
After having arrived at the derived quantity of interest the `gamma_method` can be called as detailed in the following example.
Example:
```python
my_sum.gamma_method()
print(my_sum)
> 1.70(57)
my_sum.details()
> Result 1.70000000e+00 +/- 3.89934513e+00 +/- 5.84901770e-01 (229.373%)
> t_int 3.72133617e+00 +/- 9.81032454e-01 S = 2.00
> Result 1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)
> t_int 2.71422900e+00 +/- 6.40320983e-01 S = 2.00
> 1000 samples in 1 ensemble:
> · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
```
The standard value for the automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the `gamma_method` as parameter.
@ -85,8 +87,8 @@ Example:
```python
my_sum.gamma_method(S=3.0)
my_sum.details()
> Result 1.70000000e+00 +/- 3.77151850e+00 +/- 6.47779576e-01 (221.854%)
> t_int 3.48135280e+00 +/- 1.06547679e+00 S = 3.00
> Result 1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)
> t_int 3.29909703e+00 +/- 9.77310102e-01 S = 3.00
> 1000 samples in 1 ensemble:
> · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
@ -108,8 +110,8 @@ Example:
```python
my_sum.gamma_method(tau_exp=7.2)
my_sum.details()
> Result 1.70000000e+00 +/- 3.77806247e+00 +/- 3.48320149e-01 (222.239%)
> t_int 3.49344429e+00 +/- 7.62747210e-01 tau_exp = 7.20, N_sigma = 1
> Result 1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)
> t_int 3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20, N_sigma = 1
> 1000 samples in 1 ensemble:
> · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
```